Intersect Edges Mk3 (#4144)

* edges intersectect numpy alg_1

* docs images and table fixes

* table fix 2

* mk3 version 3d algorithm and more

data_structure.py

@@ -37,6 +37,7 @@
     float64,
     int32, int64)
 from sverchok.utils.logging import info, debug
+import numpy as np
 
 
 DEBUG_MODE = False
@@ -1099,6 +1100,30 @@ def has_element(pol_edge):
         return True
     return False
 
+
+def cross_indices_np(n):
+    '''
+    create list with all the indices pairs
+    for n=3 outputs a numpy array with:
+        [0,1]
+        [0,2]
+        [1,2]
+
+    '''
+
+    nu = np.sum(np.arange(n, dtype=np.int64))
+    ind = np.zeros((nu, 2), dtype=np.int16)
+    c = 0
+    for i in range(n-1):
+        l = n-i-1
+        np_i = np.full(n-i-1, i, dtype=np.int32)
+        np_j = np.arange(i+1, n, dtype=np.int32)
+        np_a = np.stack((np_i, np_j), axis=-1)
+        ind[c:c+l, :] = np_a
+        c += l
+
+    return ind
+
 def no_space(s):
     return s.replace(' ', '_')
 

docs/nodes/CAD/CAD_index.rst

@@ -6,6 +6,7 @@ CAD
    :maxdepth: 2
 
    crop_mesh_2d
+   edges_intersect_mk3
    edges_to_faces_2d
    merge_mesh_2d
    merge_mesh_2d_lite

docs/nodes/CAD/edges_intersect_mk3.rst

@@ -0,0 +1,128 @@
+Intersect Edges
+===============
+
+.. image:: https://user-images.githubusercontent.com/28003269/70894030-a7c74080-2005-11ea-8594-dced40b05c03.png
+
+Functionality
+-------------
+
+The node is designed for finding intersections of inputs edges and returns mesh based on intersection result.
+
+This node contains several algorithm of finding edge intersections:
+
+**3D algorithm:**
+
+This is a brute force algorithm written in NumPy, it is pretty fast and pretty consistent but can produce double points that can be
+removed with the remove doubles toggle. It ignores overlapping edges.
+
+**2D algorithms**
+
+**Alg_1**
+
+Brute force algorithm that exposes every pair of edges to a mathutils function called 'intersect_line_line'. Does not check
+if there are repeated points. It ignores overlapping edges
+
+**Np**
+
+This is a brute force algorithm written in NumPy, it is pretty fast and pretty consistent but can produce double points that can be
+removed with the remove doubles toogle. It ignores overlapping edges
+
+**Sweep line algorithm**
+
+This algorithm is based on `sweep line <https://en.wikipedia.org/wiki/Sweep_line_algorithm>`_ approach:
+
+It can handle big number of edges but if there are too much intersection the performance can slow down dramatically.
+For example if each input edge intersect with every others. In this case only few edges can be handled by this node.
+
+- The algorithm does not produce double points.
+- It is less robust and can give an error.
+- For this algorithm epsilon parameter on N panel is more important. If you get an error you can try to change the parameter to fix.
+
+Prefix 2D means that the node expects from input any kind of flatten mesh
+but it does not mean that the mesh should only lay on XY surface.
+Input mesh can below or above XY surface or even can be tilted relative one.
+
+The algorithm of finding new intersection is like this:
+
+It takes two edges, removes Z coordinates and finds their intersection.
+But after intersection is found it projects intersection point back onto one of the given edges.
+This means that input mesh still should be flat but it can be located in space however you like.
+Only location of input flatten mesh along Z coordinate will bring the error.
+
+**Blender mode**
+
+This mode is using internal Blender function from `mathutils` module.
+It is pretty fast with not big number of intersections (about 1000)
+but is quite unstable and can cause crash of Blender easily.
+Also it is not design for such cases where one edge is intersect with all or most of all other edges. Use with care.
+It's available only with Blender 2.81+
+
+
+Benchmark of 2D algorithms
+--------------------------
+
+Three different test to determine the efficiency of the algorithms.
+- Random Segments: Segments between random vectors
+- Star Segments: Rotated segments from a center point (every segments intersects with the rest of segments in the center)
+- Spine Segments: Parallel Segments intersected with a middle segment that cuts them in the center.
+
+.. image:: https://user-images.githubusercontent.com/10011941/120835106-30bc9980-c564-11eb-93c5-bdbabd1a63fe.png
+
++-----------+-----------------------------------+-----------------------------+-----------------------------+
+|Test       | Random Segments                   | Star segments               | Spine Segments              |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Edges In   |   100  |   1000   | 10000         |    100 |    1000 |    10000 | 100    | 1000    | 10000    |
+|Intersec.  |   1299 |   127892 | 12355630      |      1 |       1 |        1 | 100    | 1000    | 10000    |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Alg_1      |   6 ms |   694 ms |      74872 ms | 15 ms  | 2125 ms |      SC* | 3 ms   | 226 ms  | 22618 ms |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Alg_1 + RD*|  10 ms |  1477 ms |     226240 ms | 25 ms  | 3300 ms |      SC* | 4 ms   | 246 ms  | 22626 ms |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Sweep Line | 900 ms | 76700 ms | SC*           | 53 ms  | 778ms   | 2000 ms  | 81 ms  | 1200 ms | 15500 ms |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Blender    |   3 ms |   650 ms | 112240 ms/BC* | 0.6 ms | 20ms    | 10643 ms | 0.8 ms | 12 ms   | 1100 ms  |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Np         |   4 ms |   635 ms |     316970 ms |   6 ms | 1760ms  |      SC* |   3 ms | 160 ms  | 6466 ms  |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+|Np + RD*   |   9 ms |  1281 ms | 419789 ms/BC* |  18 ms | 3052 ms |      SC* |   5 ms | 168 ms  | 6580 ms  |
++-----------+--------+----------+---------------+--------+---------+----------+--------+---------+----------+
+
+*BC = Blender Crash
+*SC = Blender Crash + Partial System Crash
+
+
+Inputs
+------
+
+Verts and Edges only. Warning: Does not support faces
+
+
+Parameters
+----------
+
+**Include 'On touch'** : consider a valid intersection when one end of the edge lays on another edge.
+    Generates double points so if active "remove doubles" switch is recommended. Only for Np and 3d mode
+
+**Doubles**: Merges points that are closer than the defined distance. Only for Alg_1, Np and 3d mode
+
+
+Parameters N-panel
+------------------
+
+Epsilon - For comparing float figures. Does not effect on performance.
+
+Big data Limit - Number of incoming edges where the node will switch to a slower-but-safer implementation of the algorithm (for Alg_1)
+
+
+Outputs
+-------
+
+Vertices and Edges, the mesh does not preserve any old vertex or edge index ordering due to the Hashing algorithm used for fast intersection lookups.
+
+
+Examples
+--------
+
+.. image:: https://cloud.githubusercontent.com/assets/619340/2811581/16032c72-ce26-11e3-9055-925d2cd03719.png
+
+See the progress of how this node came to life `here <https://github.com/nortikin/sverchok/issues/109>`_ (gifs, screenshots)

docs/nodes/modifier_change/modifier_change_index.rst

@@ -14,7 +14,6 @@ Modifier Change
    relax_mesh
    delete_loose
    mesh_clean
-   edges_intersect_mk2
    poke
    extrude_edges_mk2
    extrude_separate

index.md

@@ -464,7 +464,7 @@
 
 ## CAD
     SvBevelNode
-    SvIntersectEdgesNodeMK2
+    SvIntersectEdgesNodeMK3
     SvOffsetNode
     SvInsetSpecialMk2
     SvInsetFaces